Four times the sum of a number and two is -68. What is the number?


Four times the sum of a number and two is -68. What is the number?

Translating Word Problems Into Equations:

In mathematics, we often need to convert words into mathematical expressions, symbols, and equations. This is commonly done when given a word problem. We use the information in the problem to set up an equation in the unknown value of the problem, and then we solve the equation to solve the problem.

Answer and Explanation:

Let's start by letting the number in question be x. We are given that four times the sum of the number, x, and 2 is -68. Thus, 4 times (x + 2) is equal to -68. We can write this as an equation as follows:

  • 4(x + 2) = -68

Now, we solve this equation in order to find x, which is the number in question. First, we use distribution to simplify the left-hand side of the equation.

  • 4x + 8 = -68

Subtract 8 from both sides of the equation.

  • 4x = -76

Divide both sides of the equation by 4.

  • x = -19

We get that x = -19, so the number in question is -19.

Learn more about this topic:

Translating Words to Algebraic Expressions

from Algebra I: High School

Chapter 8 / Lesson 17

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